Extremal flow convergence conjecture for positive Kähler surfaces

Let $(M,J)$ be a complex surface of positive first Chern class polarized by a Kähler class $\Omega$. The positive first Chern class convergence conjecture. There exists an initial condition for the extremal flow equation such that the solution exists on $[0,\infty)$ and, as $t\rightarrow\infty$, converges to an extremal metric of positive scalar curvature representing $\Omega$. This is a proposed global-existence and convergence statement for extremal metrics on positively polarized complex surfaces.